I'm struggling to reconcile David Hume's critiques of science and religion. On the one hand, he suggests that our application of cause/effect to natural phenomena is problematic since it ammounts to simply equating the present with the past. On the other hand, he warns us against believing in second-hand accounts of miracles since they are interruptions of natural law. Isn't our use of causal reasoning the way we determine the characteristics of natural law? Is this an inconsistency in his argument and, if so, does he address it anywhere?

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Good question. You are pointing out an apparent contradiction. Hume seems both to say that we have no good reason to rely on induction (predicting the future based on the past), and yet that we should rely on it when we reject belief in miracles.

What Hume says about causal reasoning is that we never have sufficiently good reason to believe present predictions based on past experience. We can only justify induction by appeal to induction itself, but that is arguing in a circle. So we have no good reason to believe that the conclusions of induction are true. Nonetheless we instinctively make and believe the predictions, anyway. We can't help it. So we make a virtue of necessity and rely on these predictions. That is how we come to believe in natural laws. Now comes the part about miracles that are supposed to be violations of these laws. Based on past experience, it is more likely that a report of a miracle is mistaken than it is that the laws were really violated. So if we rely on our instinct to reason from experience, we will reject the greater miracle and believe that the report is mistaken. Hume thinks that human experience also shows that people who rely on experience in this way tend to be happier and longer-lived that people who rely on other ways of coming to belief, such as superstition or wishful thinking. So, if one wants to be happier and longer-lived one should rely on experience.

So if it is simply the truth we are after, we have no sufficiently good reason to use induction. But we can't help but use it, and we can't help but believe its results. Since we want to be long-lived and happy, we at least have good practical reasons to use induction, for instance in the case of reported miracles. This is what Hume is saying, so he isn't inconsistent after all.

Yes, that's a good point. It is true that Hume's practical recommendations are based on inductive claims that he can't ultimately justify. However, he is relying on the natural force of appeals to induction, not their epistemic justifiability. So he is still not relying on the justifiability that he denies.

Sorry to be a pest, but I still don't see how Hume escapes the problem. The claim that appeals to induction have natural force is itself an inductive claim: not a historical report of the force such appeals have had but a generalization about the force they continue to exert even on people the claimant has never met. So Hume seems to rely on the existence of a force when, by his own lights, he has no justification (not just ultimate but any justification) for believing that it exists. It looks as if Hume has to soften his critique of the justification of inductive beliefs or else stop arguing for the practical rationality of relying on induction.

If I may complicate things a bit: I don't question the scholarly accuracy of Prof. Baxter's reply on behalf of Hume, but I'd point out that he attributes to Hume a handful of inductive claims, for example: "We instinctively make and believe...predictions, anyway. We can't help it"; "People who rely on experience in this way tend to be happier and longer-lived than people who rely on other ways of coming to belief." Those are claims about human tendencies: not simply historical reports about how things have gone but inductive generalizations about how things (will) go under normal circumstances. If they were merely historical reports, we'd expect them to use the past tense rather than the present tense ("make," "believe," "rely," "tend"). Since they're inductive claims, by Hume's own lights we have no good reason to believe them. So it would seem, on this reconstruction of it, that Hume's argument for the practical rationality of our relying on induction contains premises he thinks we have no reason to accept. Maybe there's a tension in Hume's view after all?